Question

A lease valued at $24,000 requires payments of $4,500 every 3 months. If the first payment is due 2 years after the lease was signed and interest is 12% compounded quarterly, what is the term of the lease? Round up to the nearest quarter.

A) 2.75 years
B) 3 years
C) 3.25 years
D) 3.5 years

Answer 1

The term of the lease is 3.25 years.

Step-by-step explanation:

To find the term of the lease, we need to calculate how many payment periods it will take to pay off the lease. The lease is valued at $24,000, and the payments are $4,500 every 3 months. The interest is 12% compounded quarterly.

First, let's calculate the number of payment periods using the present value formula: PV = R*(1 - (1+i)^(-n))/i, where PV is the present value, R is the periodic payment, i is the interest rate per period, and n is the number of periods.

Plugging in the values, we have $24,000 = $4,500*(1 - (1+0.12/4)^(-n))/(0.12/4). Solving for n, we get n = 9.75. Rounding up to the nearest quarter, the term of the lease is 9.75 quarters, which is approximately 3.25 years.